The present invention relates to highly uniform magnetic fields, such as for nuclear magnetic resonance (NMR) imaging and the like, and, more particularly, to a novel method for homogenizing a static magnetic field over an arbitrary volume, by the use of electrical shimming coils to provide correction fields of magnitude determined by a single measurement of that static magnetic field over the surface of a sphere encompassing all of the volumes of interest.
It is well known that a static magnetic field is often required to have an essentially constant magnitude over a certain volume, as, for example, the main static magnetic field utilized in NMR imaging. In such usage, it is known that the Larmor, or resonance, frequency .omega., for a particular nuclear species, is given by the formula .omega.=.gamma.B.sub.O, where .gamma. is the gyromagnetic ratio for that nuclear species and B.sub.O is the total magnetic field magnitude to which a nucleus is exposed at its particular location. The amplitude of the response resonance signal is determined by the density of nuclei; the actual locations of the nuclei are encoded into the response signals by impressing a set of essentially linearly-varying magnetic field gradients upon the total main static magnetic field such that the resonance frequency of nuclei at different locations is different. The resulting amplitude-frequency characteristic of the response signal is Fourier-transformed and displayed to provide a density versus location display of the desired nuclear species. In order to obtain proper location information, it is required that the static magnetic field be as homogenized as possible, i.e. have as little divergence from a constant value as possible over the volume in which the measurements of the sample are taking place. For this purpose, a typical magnet, for use in NMR and the like, will have a main magnet coil (which may be of resistive or superconducting nature) and will have some number N of shim coils, each of which provides a smaller-magnitude correction field over at least a part of the volume in which the field of the main magnet occurs. The inhomogeneities in the field can be characterized by a mathematical expression containing a series of terms which depend on higher and higher powers of the linear and angular coordinates. The simplest conceptual arrangement would be to have each shim winding affect only one term. In practice, each shim coil affects multiple terms of the expansion. Because of these interrelationships of the several shimming fields, it is relatively difficult to provide minimum inhomogeneity of the static field. For example, in one particular main magnet of resistive design for providing a 0.15 tesla (T) field within a cylinder of 20 cm. length and radius, the resulting inhomogeneities (after original shimming in an attempt to minimize variations in the magnetic field over the surface of a sphere, of about 45 cm. diameter, encompassing the desired imaging volume) produced the following results; for various planes measured at some distance .DELTA.Z from the central plane of the imaging plane:
______________________________________ .DELTA.Z .+-.0 cm .+-.2 cm .+-.4 cm .+-.6 cm .+-.8 cm .+-.10 cm homo- 50 ppm 91 ppm 180 213 ppm 263 ppm 300 ppm geneity ppm ______________________________________
It will be seen that if, for the above example, a particular experiment requires an inhomogeneity of no greater than .+-.50 ppm., then there is practically no volume over which to image the sample. Accordingly, a method for shimming the static magnetic field over some arbitrary volume, to within some maximum degree of inhomogeneity, is highly desirable.